1. Field of the Invention
The present invention relates to a digital filter designing method and device, digital filter designing program and digital filter, and more particularly, to an FIR filter and a method of designing it, which comprises a tapped delay line made up of a plurality of delayers and performs multiplying signals of the respective taps several-fold and then adding up the results of multiplication and outputting the addition result.
2. Description of the Related Art
Some kind of digital signal processing is generally performed in various kinds of electronic devices provided in various fields of communication, measurement, sound/image signal processing, medical care, seismology, and so on. One of the most significant basic operation of the digital signal processing is filtering which extracts only a signal having a necessary frequency band from an input signal in which signal and noise are mixed. For this reason, digital filters are often used for electronic devices performing digital signal processing.
As the digital filter, an IIR (Infinite Impulse Response) filter and FIR (Finite Impulse Response) filter are often used. Of these digital filters, the FIR filter is a filter provided with tapped delay lines made up of a plurality of delayers, multiplies signals of the respective taps several-fold and adds up the results of multiplication and outputs the addition result, and has the following advantages. First, since extreme values of a transfer function of the FIR filter exist only at the origin of the z-plane, the circuit is always stable. Second, if filter coefficients are of a symmetric type, it is possible to realize a completely exact linear phase characteristic.
When filters are categorized from the standpoint of an arrangement of a pass band and a stop band, they are classified mainly into four categories of low-pass filters, high-pass filters, band pass filters and band elimination filters. The basic element for an IIR filter or FIR filter is a low-pass filter and other high-pass filter, band pass filter and band elimination filter are derived from the low-pass filter by carrying out processing such as frequency conversion.
By the way, the FIR filter uses impulse response expressed by a finite time length as a filter coefficient as is. Therefore, designing an FIR filter means determining filter coefficients so as to obtain a desired frequency characteristic.
Conventionally, when the low-pass filter as the basic element is designed, filter coefficients of an FIR filter with respect to the respective taps are obtained by carrying out convolutional calculations, etc., using a window function or Chebyshev approximation, etc., based on the ratio of a sampling frequency and a cutoff frequency. Then, a simulation is performed using the obtained filter coefficients to correct the coefficient values as appropriate while checking the frequency characteristic to thereby obtain a low-pass filter having a desired characteristic.
Furthermore, when the other filters such as high-pass filter, band pass filter, band elimination filter are designed, a plurality of low-pass filters as the basic elements are designed using the above described procedure first. Next, by carrying out operations such as frequency conversion by combining those low-pass filters, an FIR filter having a desired frequency characteristic is designed.
However, the filter frequency characteristic obtained using the conventional design method depends on the window function or Chebyshev approximation, and therefore if these are not set properly, it is not possible to obtain a satisfactory frequency characteristic. However, it is generally difficult to set a window function or approximate expression appropriately. That is, the above described conventional filter design method requires a skilled technician to design the filter at much expense in time and effort and has a problem that it is not possible to design an FIR filter with a desired characteristic easily.
Furthermore, even if it is possible to design an FIR filter having substantially a desired characteristic, the number of taps of the designed filter becomes enormous and the coefficient values become extremely complicated and random values. For this reason, there is a problem that a large-scale circuit structure (adders, multipliers) is required to realize such a number of taps and coefficient values. Furthermore, there is also a problem that when the designed FIR filter is actually used, the amount of calculation becomes very large and processing load becomes heavy.
The present invention has been implemented to solve such a problem and it is an object of the present invention to make it possible to easily design an FIR digital filter having a desired frequency characteristic.
Furthermore, it is another object of the present invention to provide an FIR digital filter capable of realizing a desired frequency characteristic with a small circuit scale and with a high degree of accuracy.